The post Math Circle Continuation and Changes appeared first on Harmony Learning Community.

]]>Greetings to current and former Math Circle families,

A lot is new in the world of the Math Renaissance (formerly Talking Stick) Math Circle:

- New name, location, website
- New course schedules
- New way to subscribe to blog
- New podcast
- Gratitudes

Here are the details:

- Our new home: mathrenaissance.com.
- Course schedules for the fall and winter 2021-22 are posted. The overarching theme for 2021-22 is “Axioms of Mathematics.” We’ll explore the differences between axioms, conjectures, theorems, and proofs. (An axiom is a self-evident truth, something that we assume to be true without having to prove it. You can’t prove something from nothing so we have to start somewhere.) We’ll delve into set theory, formal logic, Euclidean geometry, symmetry, isomorphism, cognitive science, number theory, and more. Douglas Hofstadter’s Pulitzer-Prize winning book
*Gödel, Escher, Bach: an Eternal Golden Braid*will be a guiding influence. In various courses, we’ll take intermissions from these studies to engage in mathematical games, unsolved problems, and applied mathematics. - After today, this Math Circle blog will no longer be distributed via the Harmony/Talking Stick site. You can resubscribe via the RSS feed on the mathrenaissance.com site or email me through the contact form if you want to subscribe via email instead.
- Rachel and I visited the New Books Network podcast to talk about math education. You can take a listen here! (You also can hear us at #kidslabpodcast.)
- As you may know, Talking Stick Learning Center has reorganized into Harmony Learning Community. I am filled with gratitude for the people here who have supported Math Circle over the past decade-plus: co-directors, parents, students, board members, and many more. Thank you for making a difference in the world!

With warm regards for all of your encouragement and support,

Rodi

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]]>The post Why We Changed Our Name appeared first on Harmony Learning Community.

]]>When I gave a budding homeschooling organization the name Talking Stick back in 2005, I was really pleased with myself. It harkened back to an ancient tradition of a kind of democratic, consensus-based practice of making sure every voice is heard. And that’s how I wanted the organization to be: that every participating youth had a say in how they would spend their time and energy while at Talking Stick. The stick need not be literal (especially if people poke each other with it). It just is about a “sense of the meeting”, as Quakers like to say.

Fast forward to 2017 when my teenage offspring gives me a lesson on some mysterious phenomenon called, “cultural appropriation”. I was like, shouldn’t all cultures share valuable practices and learn from one another? My youth went on to point out that when an extreme historical and current imbalance of power is at play, cultural appropriation becomes another destructive and disrespectful act of the oblivious white dominant culture.

The talking stick is a tradition in some Native American and African cultures. White people went around the world touching everything we could reach and saying “Mine! Mine! Mine!” leaving cultural and economic devastation in our wake. We used “Guns, Germs and Steel” (a title of a book by Jared Diamond that I recommend) to dominate in whatever ways that met our insatiable needs. Every white person continues to benefit in multiple ways from this white supremacy.

We as an organization are now holding ourselves accountable to be wary of our use of any other cultures’ terms and practices. I know not everyone will agree with this decision, because there are those that argue that as long as the appropriation is positive, it is okay. However, while I meant no offense and was in no way using the practice in a negative or derogatory way, the use of the term, Talking Stick, is problematic and ironic in that white people have a legacy of denying other cultural groups their languages and traditions and attempting to assimilate them into white culture. Then we turn around and use aspects of their cultures without permission.

As we move on to a new phase in our organization’s path, we are excited to start fresh with a new name that has connotations of social connectedness and collaboration. One that recognizes many diverse voices and aims to bring them together simultaneously in a balanced and respectful way to form a cohesive whole. Harmony is a simple and yet powerful term that we hope participants will enjoy using for years to come.

Katie O'Connor

Director

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]]>The post Human Trafficking, COVID, and Graph Theory appeared first on Harmony Learning Community.

]]>**Isomorphic problems**

“Aw, are we talking about human trafficking again? I don’t want to feel sad,” said F at the beginning of the session following the human-trafficking discussion. I was grateful to F since I wasn’t sure whether to continue that topic or move to something else. Thanks to his comment, I knew what to do.

The planned follow-up activity to the previous week’s was to use US highway maps and graph theory to analyze travel between states. * I asked the group how we could talk about the same mathematical content in a context other than slavery. In other words, how to change the problem without changing the math. The students rose to the occasion with multiple ideas – a car with money falling out of it, something about solar energy, something else about a bus. They wrote these new problems and then we then shifted gears to other topics for the rest of the day.

I’ve been thinking about F’s question ever since he asked back in February.

**COVID**

Once the pandemic hit and my daughter J’s school district switched to virtual learning, several of her teachers assigned projects related to COVID: things like the math and science of disease spread, etc. I was concerned because she and many students experienced increased depression related to the pandemic (isolation, fear, etc – nothing you haven’t heard about or experienced, I’m guessing). Some students I knew became sad and anxious when tackling these assignments. I talked to my friend R, a therapist, about this. R felt very strongly that schools should be a sanctuary away from immersion into pandemic studies, since students were living it at home. She did not think schools should do lessons centered around COVID. R, of course, was looking at this from a mental-health perspective: school as a place of safety when some students were saying that pandemic-related lessons scared them.

OTOH, some mathematicians I collaborate with were advocating strongly for presenting to students the mathematics of epidemiology. Many of their students and students’ families did not have access to accurate information about how COVID spread, how virulence works, the benefits of testing, etc. Here was an excellent chance for natural learning about math in a relevant context. And for mathematics to be a vehicle to get important health info home to families.

I came up with a grand plan to ask a variety of therapists, teachers, mathematicians, and parents for their thoughts and then to write about it here. Of course I got caught up in the change in lifestyle the pandemic has wrought, so never followed through. J’s school is no longer studying pandemic-related topics, although some schools and colleges are. This morning I asked her to apply her 20/20 hindsight to the matter: she said “it was a good idea (to study this topic) in the beginning of the pandemic but not now,” that the pros outweighed the cons initially only.

Regarding COVID: I still wonder what the right thing to do is/was in terms of weighing the emotional versus the intellectual/practical impacts.** Regarding human trafficking: can a certain context diminish a student’s enjoyment of mathematics, even make them not want to come to Math Circle? Regarding both: by exploring these topics with students, are we saving lives, which probably trumps all? I would like to see some discussion, analysis from psychology, and educational research on these questions. Please point me toward it if you know of it. And let me know what your thoughts are.

**Graph Theory**

In her email about the math of human trafficking, B reported that she was “struggling to apply math concepts to this topic.” She read in my blog***

*"Suppose law enforcement has enough employees to focus on just four cities in the US. How should they choose which ones? M suggested (and the others agreed) that we can choose the cities with the most lines, in other words, the vertices with the most edges. In other words, we could calculate the degree of each vertex on the graph." *

Her question was “Would you mind explaining why each vertex's degree on the graph can represent the city with the most lines?” I realized others reading this might wonder the same thing. Here is my reply:

*Please let me know if I am misunderstanding your question and answering something else! I suspect that your confusion may come from the terminology that I am using because in this course we were applying the math topic of graph theory, not geometry. There is some overlap in terms between these fields. Are you familiar with graph theory? A good quick intro to it is here: https://www.mathsisfun.com/activity/seven-bridges-konigsberg.html*

*Also, if you haven't already, take a look at the photo on the blog post under the heading "Results and Reaction." Take a look near the center of the image of the boardwork where it says "NY" with the number 6 in a circle. NY indicates the location of New York City. It is, in graph-theory language, a vertex on the graph. There are 6 lines coming out from the NY vertex. Each of these are called edges. These 6 edges/lines indicate flights. Can you see the line connecting NY to Kingston? This line/edge means that one can fly from NY to Kingston on one of the airlines we investigated. Kingston is another vertex (point). The "degree" of the vertex (point) means how many lines (edges) originate there. NY has 6 edges, or a degree of 6, because we drew 6 lines representing flights from NY.*

Thank you for reading and thinking about these things! I’m wishing all of you good health in the new year.

Rodi

NOTES * This planned follow-up activity is described in depth on pages 87-88 of Mathematics for Social Justice: Resources for the College Classroom.

** I also wonder about the specifics of studying this topic in a public school where students can’t opt out. In my Math Circle on human trafficking, I was able to give trigger warnings to students and their grownups so people could opt out, request that I not cover this topic, or process it at home outside of the sessions.

*** The original blog post is here: https://talkingsticklearningcenter.org/reducing-human-trafficking-through-math/. I had introduced students to graph theory in week one of this course, which I blogged about here: https://talkingsticklearningcenter.org/intro-to-voting-theory/ (scroll down to “Getting away from Numbers”).

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]]>The post Math Circle Scheduling and Enrollment Update appeared first on Harmony Learning Community.

]]>We’d like to get scheduling input from any of you who would definitely sign your young people up for the other three classes. If this is your situation, feel free to email Rodi at rodi@talkingsticklearningcenter.org, with info about your availability on weekdays between 10-2 during the time of the relevant course.

We are hoping that sometime during this year, and we will be able to gradually increase the class size to allow more participants.

Thank you for your patience!

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]]>The post Math Circle FAQs 2020-21 appeared first on Harmony Learning Community.

]]>You can see the list and register here: https://talkingsticklearningcenter.org/math-circle-fall-2020/

**How and when will the class time be determined?**

For the first course of the year (The Cookie Monster Problem) the exact time will be announced at the end of the day on Thursday, September 10. Families who definitely intend to enroll if the schedule works can email Rodi (rodi@talkingstickleaningcenter.org) directly with schedule preferences (time, day of week) by Wednesday, September 9. We will do our best to schedule the course to meet the needs of the participants. This particular course will meet on Tuesdays, Wednesdays, or Thursdays between 10am-2pm.

On September 10, we will post schedule info on the Talking Stick Math Circle Blog, on the Talking Stick Website, on the Talking Stick Facebook Page, and also to Rodi’s Math Circle email distribution list. (Email Rodi to get on this list if you’re interested.)

We welcome input on schedule preferences for the future courses as well.

**How is enrollment prioritized?**

- Families with Talking Stick Family Membership: https://talkingsticklearningcenter.org/covid-19-updates-2/
- If spots remain, local families who have previously participated in the Virtual Talking Stick Math Circle
- If spots remain, local families who have previously participated in the In-Person Talking Stick Math Circle
- If spots remain, local students (homeschoolers and school students are all welcome)

**How do I get on the waiting list?**

Email Rodi at rodi@talkingsticklearningcenter.org

**When will the courses open up to the waiting list?**

If not all spots have been taken by families with Talking Stick Memberships, students on the waiting list will be offered spots 48 hours before the first session. If you are on the waiting list, make sure to have a plan to obtain the required materials before the course begins.

**Will the enrollment cap always be just 6 students?**

We hope to increase class size once we can meet in person (if a larger group is COVID-safe).

**What are the participant requirements for meeting virtually?**

Each student should have a laptop or desktop computer with a mouse or a pen tool. It’s difficult for students to do a hands-on math workshop via Zoom on a tablet. The device should have a working microphone and speaker, or students can wear a headset. Ideally we’d like students to have an adult within voice-range to offer support with tech and supplies as needed. Enrolled families must sign a liability form before attending.

**What are the participant requirements for meeting in-person outdoors?**

We hope to transition from virtual meetings to in-person outdoor sessions when safe. We require all participants (students and all adults present) to wear masks, social distance, and hand wash/sanitize.

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]]>The post ONLINE Math Circle starts this week appeared first on Harmony Learning Community.

]]>*

In this course, students will explore three underlying themes: math can be used to model real life; mathematical structures underlie much in life; and the study of mathematics meets many human emotional needs. Planned activities will include the M&M Death and Immigration Problem, Conway’s game of Life, the Fold and Cut Theorem, Fermi problems, and the Pigeonhole Principle. This course is inspired by and Eric Dermaine’s work on recreational mathematics and especially by Francis Su’s work on mathematics for human flourishing. Underlying mathematical concepts and skills include number sense, pattern-seeking, the ability to generalize, prediction, geometry, estimation, algebraic thinking, proof, algorithms, iteration, and self-replication.

We will adapt the topics to best suit students' needs. Whether in-person or online, Math Circles are organic and are co-created moment by moment.

LOGISTICS:

- Recommended age range is 10-12.
- Sessions meet on Thursday afternoons from 1-2pm from 4/23-5/14 for 1 hour on Thursdays from 1-2pm. (4 sessions, 4 hours of instruction.) The course might be extended to 6 weeks for interested students. The above description is at least 6 weeks of content!
- Sessions will run on Zoom. (Zoom classroom donated by Natural Math Zoom, with security features optimized by Natural Math.)
- Enrollment is limited to 6 students. Currently 4 are enrolled. Enrollment will be prioritized for prior Math Circle participants, Talking Stick Learning Center students, and then will open to others.
- Tuition for the course of 4 sessions is on a sliding scale from $80-$100 total, according to families’ ability to pay.
- Initially a must be in the room with the student during the sessions, but we can move to students only with appropriate liability releases signed.
- Students will need to bring some supplies occasionally (scissors, paper, printouts, M&Ms, etc.).
- Email rodi@talkingsticklearningcenter.org for more information or to enroll.

* mathematical art credit: Joanna Steinig

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]]>The post Reducing Human Trafficking through Math appeared first on Harmony Learning Community.

]]>On the day of the class, not everyone had arrived by class time, so I began with some other topics. “But I thought we were talking about human trafficking today,” questioned F. We soon turned out attention to that issue.

“What is that?!” asked A about the box that said “Flash Gordon” on the table. After a quick discussion about who Flash Gordon is, I explained that this Flash is a bobblehead doll, and that we were going to use his bobbling to help us focus. “Why?” wondered the students. I explained that a focusing activity can help us bring our best to conversations about emotional topics. We then proceeded to watch Flash bobble until he stopped. He. Didn’t. Ever. Stop. So we began our conversation quietly.

I gave some background statistics on human trafficking and students contributed what they know about it. I then passed around a picture of former victim and present author Zana Muhsen, explaining to students that in math and science we can get so focused on the interesting questions about a problem that we can forget that we are talking about human beings. We kept the photo of Zana in the center of the table for the whole session.

**PUTTING MATH TO WORK**

“Math can be a tool to lessen human suffering,” I said to introduce the math problem:

*“How can law enforcement know where to focus their
efforts to reduce or stop human trafficking in the US?”*

(This lesson was first used by and published by Dr. Julie Beier of Earlham College; I did things just a little bit differently. In our course, we did not do a deep study of human trafficking before getting into the math. We did not preface the presentation of the problem with an in-depth study of graph theory; we did do the famous Konigsburg Bridge graph-theory problem several weeks before. Also, I did not instruct the students to “determine the major entry points using airline maps;” instead I hoped that the students would come up with this strategy themselves, which they mostly did.)

The students had a lot of ideas for law enforcement and the discussion moved into how the victims, who are mainly from Central America, the Caribbean, and Asia, get to the US. Once students realized to target cities with a lot of flights from those regions, I passed out airline maps. Students examined these maps (with help from parents) to create a master map. This map was essentially a graph theory graph with cities/regions as vertices and airline paths as edges. I used these mathematical terms for the rest of class.

“Suppose law enforcement has enough employees to focus on just 4 cities in the US. How should they choose which ones?” M suggested (and the others agreed) that we can choose the cities with the most lines, in other words, the vertices with the most edges. In other words, we could calculate the degree of each vertex on the graph.

**THE RELIABILITY OF MATH MODELLING?**

Before getting to work on that calculation, students had a lot to say about the lack of accuracy on our graph. For one thing, we had only examined flights from 2 US, 2 Asian airlines, 1 Mexican, 1 Latin American, and 1 Caribbean airlines. “How many airlines are there in the US, in Asia, etc.?” wondered the students. Parents, our in-class researchers, looked this up. Not surprisingly, we had a dramatic underreporting of airlines and cities. Also, the printouts of the maps were a bit hard to read, so we couldn’t even include every flight from our 7 airlines.

“Would it be okay for law enforcement to take action based upon our data and analysis?” Absolutely not, said the students. “Before we do our mathematical analysis, then,” I explained, “we have to state and write down our assumptions.” Students stated that the graph is “not thorough,” “a dramatization,” “an oversimplification,” and based upon “incomplete data.” We were all emphatic that any conclusions were drew were just an exercise, that real-life math modelling required more thorough and more accurate data.

**RESULTS AND REACTION**

Finally, students were ready to calculate degree and choose the four cities to target. Three cities exceeded the others in degree: Anchorage, San Francisco, and New York City. But four cities tied for fourth place: Seattle, San Francisco, Orlando, and Dallas. “How should we choose if we are not going to complete the data with more flight maps?” Students suggested various methods. M suggested we choose Seattle based upon some other data she had seen, so we did.

“Let’s suppose that you work for law enforcement in one of these cities. How could you use math to further focus your investigation beyond the airports?” I asked. Students started to discuss this a bit until a student asked “What time is it?”

It was 4:51. We had been at it since 3:30. We usually start cleaning up at 4:55. Everyone was surprised by how late it was. There was no time for further discussion or another activity.

A said, “I guess time flies when you’re having fun,” but he said it in a wistful voice. The students, who usually exit class in upbeat moods, were a bit subdued. I could see that they would probably need time to process the emotional content of this lesson. I acknowledged this and told them (and the parents present) to please talk about this more at home.

I did want to end class on an upbeat note, so I told students that one activity I want to do next week is to try out another voting method, and that I want to have the puppets vote for a place to go on vacation. This (puppets!) perked people up quickly – specifically thinking about what kind of places that puppets might want to go on vacation. (So far, the students’ list includes Sesame Street, F’s house, Disneyworld, washing machine and then on top of a laundry basket, Turkey, toy shop, and Stonehenge.) F asked if he could bring someone from home (not a puppet but similar) in next week for the voting, and I said, “the more, the merrier.” I encourage all students to bring in more voters, especially since we’ve been talking the whole course about voter turnout issues!

I haven’t yet decided whether we should continue with this topic. There is a lot of deeper mathematics to explore, but OTOH we only have 2 sessions left and one student already missed this lesson. We may want to explore other topics and finish off our exploration of voting theory. Parents, let me know if you or your students have strong feelings either way.

I am filled with gratitude for the parents who helped out in class and the parents who were not able to come but trusted me to cover the topic appropriately with your children. I am grateful to have had the chance to do it.

**OTHER TOPICS**

As we were waiting for everyone to arrive, we talked about voting-theory math in this week’s news. We looked at articles about

- How some pundits find that plurality voting in the Democratic primary problematic
- How close to representing the country demographically Pennsylvania is
- A study done on why so many people don’t vote (This prompted a student-led collaboration on figuring out what percent of the US population doesn’t vote. The article stated that about 100 million people sit out elections. Students decided to look up total population, child population, felon population, and were incredulous to figure out what a large portion of the population qualified to vote the non-voters comprise.)

We also did more work on the 4-color theorem. Students tried to color M’s map that previously seemed to require 5 colors. This time they did it quickly in 4.

We discussed whether there is an optimal strategy to do the work on this problem. (M started with one color and colored every region possible with that color before switching to a different color. F started with one region and colored every adjacent region before moving to a different region.) I asked again whether any maps require more than 5 colors, or could these 4-color maps be done in 3. “Are you going to tell us the answer?” asked F. (I didn’t promise, but I probably will at the last session. I don’t usually do this, but mathematicians required a computer to solve this one.)

Rodi

*For anyone who didn’t see it, here is my pre-class email to parents:

*As
you know from reading the course description of our current course, one of our
topics is human trafficking. Tomorrow we will begin our mathematical
exploration of this topic. The math involves graph theory, mathematical
modelling, and data analysis. To give the mathematics some context, we will
talk for a short bit about what human trafficking is.*

*I
am using a module that is used in a course at Earlham College, described in the
book "Mathematics for Social Justice: Resources for the College
Classroom." I will not be doing the background/contextual studies that a
college class would. In the book, Dr. Julie Beier of Earlham suggests
supporting students for the emotional content by "setting classroom
guidelines for discussion, practice with less intense topics, and starting with
silence to encourage students to bring their best self to a conversation."
She also recommends that instructors "explain the purpose of silence"
and to encourage students "to make a list of their reactions." We
have already been doing the first two suggestions and plan to do the others as
well. I do plan to start with a totally secular focusing activity - probably a
bobblehead doll. I would like to invite any of you to sit in for the topic
introduction, and to email or call me with any questions or concerns up front.*

*The
background that I will introduce is from the UN Office of Drugs and Crime
(UNODC):*

*only 63% of 155 countries providing data to the UN have "passed laws against the trafficking of people"**"approximately 79% of human trafficking is for sexual exploitation"**"approximately 79% of all victims are female"**"forced labor accounts for about 18% of the reported trafficking**"the percentage of humans trafficked that are children is 20% globally, although in some parts of the world it is as high as 100%"*

*There
is not much more known or studied about this problem, and beyond these
statistics and information about the logistics of how the transport of victims
works, I do not plan to delve into background. Students will, of course, have
questions. (Ellen, you will of course use your judgement about which questions
to research in class and which to defer to outside study.)*

*I
STRONGLY encourage you to talk with your students in advance about this if you
suspect your student will have an emotional reaction to hearing this
information for the first time.*

*Also,
feel free to respond to this email (reply to all, please) or call/text me with
any other questions or concerns.*

*Best
regards,*

*Rodi*

The post Reducing Human Trafficking through Math appeared first on Harmony Learning Community.

]]>The post Data Interpretation and Analysis appeared first on Harmony Learning Community.

]]>*“Suppose the country votes state by state on different
days; we are in Hawaii; and actual state preferences are ravioli 1%, mint
chocolate chip 12%, butter pecan 12%, mango 40%, vanilla 20%, and chocolate
15%. What voting method would each flavor lobby want?”*

*“Suppose there was a caucus with low turnout, a pushy
person there advocating for butter pecan, and a required tasting session first.
What would happen and what would be the implications?”*

I asked these questions to facilitate evaluation of the Iowa Caucus, which took place 2 days before our session. Students brought up important issues, explored possible outcomes, and moved the conversation in some unexpected, interesting directions such as the population of Hawaii, mosquito control, and how percents work. They also came up with some novel voting methods.

**PERCENTS WITH MOSQUITOES**

A had a lot of questions about how percents and percent change are calculated. In response to his question “Is it possible to have percents that are over 100%?” M came up with some examples involving mosquitoes. For instance, “The mosquito population increased by 200 percent.” “What does it mean to have minus 200 percent?” asked someone. We made up some examples with mosquito population changing over time to illustrate the calculation. Then F asked, “Why are there only 10 mosquitoes in the whole world?”

“Because this is math!” I replied. “We can make up anything we want within a system as long as we follow a consistent set of rules within that system.” We also talked about, as we have before, how the math itself can become clearer with easier examples.

Students also pointed out that mosquito growth isn’t linear, it’s probably exponential. Again, though, we can imagine it to work how we want it to work since this is math and our goal is precision and logic.

**THE IOWA CAUCUS**

I then handed out photos and the detailed results of the Iowa Caucus at various points in time. “What do you notice?” Students analyzed how the results varied depending upon what percent of the results had been counted. They also noted how the first alignment begets the second alignment begets delegates.

We looked at a map of results by county. “Would it be fairer if the delegates were elected proportionally to county instead of proportional to population?” All of the students were adamant that this was a terribly unfair idea. My helper Ellen and I told them that it has been and is done this way in some circumstances in the USA. Could the students guess where? J knew that the electoral college had some geographic issues built into it, but everyone was pretty skeptical of the concept of how representation is done in the Senate. Another issue that came up is how Iowa can influence the entire electorate while not necessarily representing the entire electorate in terms of various demographics.

**THE WRONG KONIGSBURG BRIDGE PROBLEM**

I accidentally presented an oversimplified version this famous problem. When I posed the question, I forgot that you have to start and end on the same side. Students made fast work of it, testing it first using an actual map and then using a graph theory map. They definitely preferred exploring the problem using graph theory, coming up with the conjectures that it is impossible to cross all the bridges once with 7 bridges in this position but possible with 5, 6, and 8. This being math, the most important questions were “Why?” and “Can you prove it?” I asked “Is it possible with 117 bridges.” The working conjectures at this point are yes if you move the bridges so that they are all parallel and no if you keep them where they are because there is an odd number. To be continued next week, with the correct problem.

**TO EXTEND AT HOME FOR THOSE WHO DESIRE:**

- Why do some of the Andrew Yang signs at the Iowa Caucus say “MATH” instead of “YANG?” (The students noticed this but we didn’t get a chance to explore.)
- Explore percent change

See you next week!

Rodi

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]]>The post Caucusing and the Four-Color Theorem appeared first on Harmony Learning Community.

]]>*“Suppose that your state is going to vote for a leader
and that all citizens and candidates only care about one issue: the law that
you can keep dairy products in your refrigerator for no more than 21 days. You
hold a caucus. What happens when the following four candidates run and the
puppets vote?*

*DAIRY-LOBBY CANDIDATE (dark blue): The soy milk industry is damaging the dairy milk industry. Our state’s workers feed their families with money earned from working with cows. I will work to make soy milk illegal, and if not illegal, pass a law against calling it “milk.”**COW-OWNER CANDIDATE (light blue): I have some cows but also have child who is lactose intolerant and needs an alternative to dairy products. I support the applying the 21-day rule to both dairy and non-dairy milk products.**HEALTH-PERSPECTIVE CANDIDATE (green): Since expired dairy milk and expired soy milk have different health consequences, the 21-day law should only apply to dairy milk. I will pass a law exempting soy milk.**NO-NANNY-STATE CANDIDATE (pink): What is the government doing in our refrigerators? The 21-day milk law should be struck down. The government has no business making and enforcing laws about how we use products.”*

First the students reacted to these candidates. Disbelief that someone would propose criminalizing the word milk applied to non-dairy beverages. Confusion about what soy milk is. Uncertainty about the word “exempt.” Laughter...

We had the puppets (so that we don’t get into discussions of student preferences) caucus for these candidates. We explored all sorts of scenarios of first and second alignment, based upon explanations from the Des Moines Register.*

After experiencing a caucus first-hand, I asked the big question: I told the students the 5 changes that Iowa was instituting this year and asked the students for conjectures on the reasons for each change.

**MAP COLORING**

Can you make a map that requires 5 colors to color? At various points students thought they did. We talked about how a mathematician’s job is to make patterns and break patterns. I walked around trying to break patterns (in other words burst people’s bubbles of hope that they had succeeded in this mission). In most cases I was able to point out a way to use fewer colors.

But there were 2 maps where I couldn’t do this quickly or easily.

I promised students that next week, they (not I) will try to reduce these student-created 5-color maps to 4—or-fewer color maps.

ANTI-PLURALITY VOTING

We played out and analyzed Wikipedia’s Tennessee capital example of anti-plurality voting. Students discussed and realized about how this method can lead to results where a more middle-of-the-road/bland/non-extreme candidate is more likely to win. “Is that a problem?” I asked. Students were split. My helper Ellen then read from an article on presidential candidate Andrew Yang’s website about voting methods.

QUESTIONS/UNEXPECTED TOPICS

Our mathematical explorations led students to pose some new questions. (Some of you may be familiar with Rochelle Gutiérrez’s work on rehumanizing mathematics. Giving students opportunities to follow their own curiosity and to connect math to other disciplines are two of the ways we can rehumanize mathematics.) Our students wondered and investigated/discussed

- HISTORY: Which candidate is a Freemason?
- ETYMOLOGY: Why is milk called milk?
- CURRENT EVENTS: Are Republicans caucusing in Iowa too, or is it just the Democrats?
- POLITICAL SCIENCE: If the Senate convicts the president and he cannot run for a second term, would the Republican party be able to field a candidate at this point, and if so, whom?

Rodi

‘* Our discussions were based upon good background info from the Des Moines Register and NPR.

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]]>Stop by to talk to staff and participants about our programs for homeschoolers ages 4-17. We will be hosting the entire open house at our Garden Classroom. We have several families attending with young people in different age groups, so we are planning to have all ages, all programs meet in one location.

To let us know that you are going to attend, please click here.

And please share this with any families you think might be interested in Talking Stick!

**DATE:** Wednesday, February 12th, 2020**TIME:** 10:00 a.m. to 12:00 p.m.**LOCATION:** The Garden Classroom at Awbury Arboretum

**The Garden Classroom**

The Garden Classroom is accessible by foot through the entrance on Ardleigh Street, northwest of Washington Lane. Please park on Ardleigh St and walk up the path across from E. Duval Street to the green classroom building.

Directions to the Garden Classroom

*Please note that other directions or GPS to Awbury Arboretum will take you to Cope House, which is NOT walking distance to the Garden Classroom.*

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